Distributive Property:

The distributive property is a fundamental property in mathematics that allows us to multiply a number by a sum or difference of other numbers by distributing the multiplication across each term. It is often represented as:

a × (b + c) = a × b + a × c

In this case, we are asked to find the product of the largest 3-digit number and the largest 4-digit number using the distributive property. Let's break it down step by step.

Finding the largest 3-digit number:
The largest 3-digit number is 999. This number consists of hundreds, tens, and units place values.

999 = 9 × 100 + 9 × 10 + 9

Finding the largest 4-digit number:
The largest 4-digit number is 9999. This number also consists of thousands, hundreds, tens, and units place values.

9999 = 9 × 1000 + 9 × 100 + 9 × 10 + 9

Applying the distributive property:
Now, let's use the distributive property to find the product of the largest 3-digit number and the largest 4-digit number.

999 × 9999 = (9 × 100 + 9 × 10 + 9) × (9 × 1000 + 9 × 100 + 9 × 10 + 9)

Using the distributive property, we can multiply each term of the first number (999) by each term of the second number (9999) and then add the products together.

999 × 9999 = (9 × 100 × 9 × 1000) + (9 × 100 × 9 × 100) + (9 × 100 × 9 × 10) + (9 × 100 × 9) + (9 × 10 × 9 × 1000) + (9 × 10 × 9 × 100) + (9 × 10 × 9 × 10) + (9 × 10 × 9) + (9 × 9 × 1000) + (9 × 9 × 100) + (9 × 9 × 10) + (9 × 9)

Simplifying the expression:
Let's simplify the expression by multiplying the numbers.

999 × 9999 = 8100000 + 729000 + 81000 + 810 + 810000 + 81000 + 8100 + 90 + 81000 + 9000 + 90 + 81

Now, we can add up all these products together to find the final result.

999 × 9999 = 99899001

Conclusion:
The product of the largest 3-digit number (999) and the largest 4-digit number (9999) using the distributive property is 99899001.

999×(1000-1)=999000-999=99811